It is often necessary to amplify an signal. A simple amplifier stage is shown in FIG. 1 wherein a field effect transistor 1 has an impedance 2 connected between its drain terminal and a positive supply rail 3. A source terminal of the field effect transistor 1 may be connected to a negative supply or ground rail either directly as shown or via a further impedance. A gate of the field effect transistor 1 is supplied with a DC bias voltage from a bias generating circuit 4 and an AC signal to be amplified which is decoupled from the bias circuit 4 via a decoupling capacitor 5.
For an ideal transconductor the current flowing in a current flow path through the transconductor would be linearly related to a control voltage applied to a control terminal of the transconductor, and the transconductor draws no current at its control terminal.
However, real transistors have characteristics which differ significantly from idealised devices. The field effect transistor is commonly used in transconductance amplifiers because it's input impedance is high. However it is well known that a field effect transistor has a drain-source current ID which for an idealised transistor exhibits the following characteristicsID=0 when Vgs−Vth<0  Equation 1where                Vgs=gate source voltage        Vth=threshold voltage of the FET        
In a so called “linear region”, also known as a “triode region” of the device characteristic where VDS is greater then zero but less than (Vgs−Vth) the drain current is as follows:
                              I          D                =                  β          ⁡                      (                                                            (                                                            V                      gs                                        -                                          V                      th                                                        )                                ⁢                                  V                  DS                                            -                                                V                  DS                  2                                2                                      )                                              Equation        ⁢                                  ⁢        2            where:                β is a constant which, amongst other things is proportional to the ratio of the FET channel width to the channel length.        VDS=drain-source voltage.        
However once VDS exceeds (Vgs−Vth) the device enters its saturation region where
                              I          D                =                              β            2                    ⁢                                    (                                                V                  gs                                -                                  V                  th                                            )                        2                                              Equation        ⁢                                  ⁢        3            Following on from these idealised equations, we see that in the saturation region, the transconductance gm is
      g    m    =                    ⅆ                  I          D                            ⅆ                  V          gs                      =          β      ⁡              (                              V            gs                    -                      V            th                          )            
However, real devices can deviate from these ideal characteristics.
FIG. 2a illustrates a transfer characteristic of a NMOS FET constructed having a gate dimension of 100 μm by 0.18 μm fabricated using a 0.18 μm CMOS technology as typically found in an integrated circuit, and showing the drain current as a function of the gate-source voltage. It will be seen that the transistor is essentially non conducting until the gate-source voltage exceeds the threshold voltage of the transistor which in this example is around 0.4 volts. From then on the current rises in a non linear manner until a gate-source voltage which is approximately 1 volt is reached and from then on the curve is approximately linear. In this final region the second and third order derivatives of drain current with respect to gate-source voltage have become reasonably small. However, these are all qualative rather than quantative assessments of the transistor's performance. It should also be noted that operating a transistor in this region can be relatively power hungry.
In these examples the drain-source voltage was held fixed at 1 volt.
The linearity of the response can be examined by looking at the derivatives of the curve IDS versus VGS shown in FIG. 2a. FIG. 2b shows the first derivative of drain current with respect to gate-source voltage, i.e. the transconductance, and it can be seen that between 0.5 volts and approximately 0.7 volts there is quite a marked change in the rate of change of current with respect to gate-source voltage corresponding to the curved area generally designated 6 in FIG. 2a. In this region the gradient of the curve looks substantially constant. However from about 1.2 volts onwards the first derivative is substantially constant. FIGS. 2c and 2d show the second derivative and the third derivative of the transfer characteristic of the transistor. These higher order derivatives represent sources of harmonic distortion when amplifying a signal, and represent sources of inter-signal mixing i.e. the creation of inter-modulation products when two or more signals having distinct frequencies are presented to the amplifier.
It is known that the distortion in small signal amplifiers can be represented by a Taylor series. If we consider only the lower order components of such an expansion, we haveID≈IDO+g1Vin+g2Vin2+g3Vin3where
      g    n    =            ⅆ              I        n                    ⅆ              V        gs        n            Where                n=1, 2, 3 . . .        
It is known that the distortion resulting from the second derivative or the distortion resulting from the third derivative can be reduced to substantially zero provided the individual transistor is biased to a specific biased voltage which, unfortunately, is unique to that transistor. Thus, if a batch of identical circuits are made in a fabrication process, tiny variations from wafer to wafer and indeed from one transistor to another transistor within the same integrated circuit would mean that each transistor would have a slightly different bias point for, for example, reducing the third order derivative to zero even though the transistors were nominally identical.
Even so, it can be seen that if a transistor is biased to a point where the 3rd derivative is zero, the second derivative is still likely to have a significant non-zero value. Therefore this approach merely trades one source of distortion for another. In circuits, like that shown in FIG. 1, where no feedback is provided, the dominant source of third-order intermodulation products (IM3) is the 3rd order non-linearity, g3 shown in FIG. 2d. reducing g3 can be achieved, for example, by biasing the transistor to the point where g3 is zero.
In circuits having feedback the situation can become more complex. For transistors having a series-series feedback scheme (i.e. an impedance placed between the source terminal and ground) then there are two dominant mechanisms giving rise to third-order intermodulation products. These are                1) 3rd order non-linearity within the transistor as characterised by g3.        2) 2nd order non-linearity as characterised by g 2.        
One might suppose that linearity could be achieved by merely operating a relatively large gate-source voltages where the drain -source current tends to become a linear function of the gate source voltage. Whilst this can work, it is a power hungry solution that is not suitable for a large number of applications, such as mobile radio or mobile telephones.
These non-linearities are particularly undesirable in amplifiers, such as radio frequency amplifiers, which may be required to amplify a relatively weak wanted signal, designated S in FIG. 3, in the presence of stronger interfering signals designated I1 and I2. In the scenario shown in FIG. 3 the frequency difference between the wanted signal S and the first interferer I1 is the same as the frequency difference between the interferer I1 and a second interferer I2. Thus non-linearities within the amplifier stage give rise to mixing of the interfering signals Iand I2 such that a new interfering signal I3 is generated within the amplifier which has the same frequency as the wanted signal S and which, as a consequence may impact on the ability of the receiver to recover the wanted signal S or which may inhibit reception of that signal completely.